Roll Control for a Micro Air Vehicle Using Active Wing Morphing

Transcription

1 Roll Control for a Micro Air Vehicle Using Active Wing Morphing Helen Garcia, Mujahid Abdulrahim and Rick Lind University of Florida 1 Introduction Relatively small aircraft have recently been receiving considerable attention in the flight test community. In particular, aircraft denoted by DARPA as a micro air vehicle, MAV, are being designed with wing span less than 6 in to operate at airspeeds less than 25 mph. Such aircraft are envisioned as expendable platforms for surveillance and data collection that can operate in dangerous or confined spaces. The University of Florida has been extremely active in the field of MAV design and testing. The team led by Dr. Peter Ifju is especially accomplished in that they have won various aspects of the Micro Aerial Vehicle Competition, sponsored by the International Society of Structural and Multidisciplinary Optimization, each year from 1999 to 22. His team has designed, built, and flown many unique designs ranging from 2 ft to 4 in wing span that are remotely piloted using vision feedback to a ground station. Most of the MAVs currently being flown at the University of Florida have a similarity; namely, these aircraft are demonstrably difficult to fly. Such difficulty is somewhat expected given that the aircraft are highly agile and maneuverable but must be flown remotely. The team is currently investigating methods of active control for the MAV that would allow autonomous operation and greatly extend the applications for which such vehicles may be considered. The use of innovative control effectors is an area being explored as an enabling technology for designing a stability augmentation system. The current generation of MAV uses traditional effectors, specifically an elevator and rudder, whose positions are commanded by the remote pilot. The elevator presents adequate effectiveness for longitudinal control but the rudder presents some difficulty for lateral-directional control. Basically, the rudder mainly excites the dutch roll mode so steering and gust rejection are really accomplished using the coupled roll and yaw motion resulting from dutch roll dynamics. Such an approach is obviously not optimal but traditional ailerons are not feasible on this type of aircraft. The concept of morphing presents several opportunities for enabling control of a MAV. Morphing is particularly appealing for twisting the wing and enabling roll control. Wing twist is actually used on the current MAV but in a passive sense. Essentially, the wing deforms under loading in flight to produce a passive washout that helps smooth the flight path. Such a concept can be extended to allow greater twists that are actively commanded to generate large roll moments. Graduate Student Undergraduate Student Assistant Professor, Department of Mechanical and Aerospace Engineering, 231 Aerospace Building, Gainesville FL, 32611, rick@mae.ufl.edu, Senior Member AIAA (Corresponding Author 1

2 This paper considers using morphing for roll control of a MAV designed by Dr. Ifju s team at the University of Florida. This vehicle has a 1 in wing span with membrane wings that are highly flexible. The open-loop responses of the aircraft are investigated using the rudder and active wing twisting. The resulting flight data is used to generate models that describe the flight dynamics. A simple stability augmentation systems is then designed that allows the aircraft to accurately track roll commands without incurring excessive yaw or sideslip. The continuing maturation of materials and controls technology is leading to consideration of morphing on larger scales for envisioned aircraft projects. Such a concept is being adopted for the Active Aeroelastic Wing to provide roll control of an F/A-18 [6]. Active morphing is a reasonable concept for full-size aircraft; however, the power and size requirements for morphing actuators, such as active materials, precludes their use on a MAV. Therefore, the morphing in this study is accomplished by directly connecting a servo, fixed in the fuselage, to points near the trailing-edge outboard of each wing. The resulting wing twist is shown to act similarly to ailerons for generating rolling moments. 2 Micro Air Vehicle This paper will utilize the micro air vehicle (MAV shown in Figure 1. Figure 1: Overhead View of the MAV The basic properties of the MAV are given in Table 1. Property Value Wingspan 1 Wing Area 29 Wing Loading 14 Aspect Ratio 3.44 Powerplant Electric motor w/ 2.25 propeller Total Weight 8g Table 1: Properties of the MAV 2

3 The flight test vehicle is based on a family of flexible-wing micro air vehicles designed by the University of Florida. The airframe is constructed entirely of composite carbon-fiber. The fuselage is a two-piece monocoque structure designed to house flight components, control effectors, and instrumentation. A conventional empennage is affixed to the fuselage with elevator and rudder control surfaces hinged to the horizontal and vertical stabilizers respectively as shown in Figure 2. Figure 2: Empennage of the MAV The wing, which is mounted on cabin struts.75 above the fuselage, is constructed using similar composite techniques as the fuselage and empennage. The leading edge consists of a single layer of carbon-fiber weave with battens of unidirectional carbon attached to the underside and extending to the trailing edge. The composite wing skeleton is covered with an extensible membrane skin of latex rubber. The resulting structure can be grossly deformed via mechanical actuation yet is capable of withstanding flight loads. The flexible nature of the wing also gives rise to the mechanism of adaptive washout which permits small changes in wing shape in response to gusty wind conditions. The MAV is equipped with instrumentation that is housed within the fuselage as shown in Figure 3. This instrumentation includes servos for actuation, sensors for measurement, and a board for data acquisition. Figure 3: Instrumentation in the MAV All sensing and actuation data is recorded using a 7 gram micro data acquisition board ( DAS developed by NASA Langley Research Center specifically for MAVs. The DAS measures 27 analog channels in addition to on-board 3-axis gyros. The data is sampled at 5 to 1Hz and is resolved using a 12-bit analog-digital converter. The data is recorded in a 4 MB flash chip on-board the DAS and is downloaded to a PC at the end of each flight. 3

4 The current study considers only the rolling response of the vehicle. Correspondingly, the initial flights record only roll rate using a Tokin 3AOB ceramic angular rate sensor. This sensor has a resolution of approximately.4547 mv/deg/s with a maximum output of 5 V. Actuation of the MAV is accomplished with three control effectors or servos mounted inside the fuselage. These devices actuate the control surfaces or wing morphing by rotating an arm and pushing or pulling a pushrod. The control surfaces of elevator and rudder are connected to the servo using a spring steel pushrod. The wing morphing is achieved by connecting the servo to the wing edge using a thin strand of Kevlar threads. The approximate range of motion for each is given in Table 2. Effector elevator rudder morphing Range of Motion to to! to Table 2: Range of Control Effectors The wing morphing is accomplished using a single servo that is attached to the trailing-edge outboard of each wing. As such, only a single wing can be morphed at any time. For instance, left actuation of the servo tensions the right-side strand to morph the right wing but the left-side strand becomes slack so no morphing affects the left wing. The amount of morphing that is achieved is demonstrated in Figure 4 and Figure 5. Figure 4: Rear View of the MAV with Undeflected (left and Morphed (right Wing Figure 5: Side View of the MAV with Undeflected (left and Morphed (right Wing 4

5 3 Open-Loop Flight Tests A series of flight tests are performed with the MAV for this project. These tests provide an immediate indication of the flight properties associated with the wing morphing. The testing also allows preliminary indication of the difficulty in piloting the MAV using the morphing as compared to the rudder. Finally, the testing generates data from which models and controllers are derived. Flight testing of the active wing-shaping MAV is performed in the open area of a radio controlled (R/C model field during which winds conditions range from calm to 7 knots throughout the flights. Once the flight control and instrumentation systems are powered and initialized, the MAV is hand-launched into the wind. This launch is an effective method to quickly and reliably allow the MAV to reach flying speed and begin a climb to altitude. The airplane is controlled by a pilot on the ground who maneuvers the airplane visually by operating an R/C transmitter. The data acquisition system begins recording as soon as the motor is powered. The aircraft design allows either rudder or wing shaping to be used as the primary lateral control for standard maneuvering. The airplane is controlled in this manner through turns, climbs, and level flight until a suitable altitude is reached. At altitude, the airplane is trimmed for straight and level flight. This trim establishes a neutral reference point for all the control surfaces and facilitates performing flight test maneuvers. The flight test maneuver of interest is a control doublet for both rudder and wing shaping controls. This maneuver is performed by commanding a constant left deflection for a certain time period followed immediately by a right deflection for the same time period and finally returning to the neutral position. Aircraft response characteristics to the control input are then determined by analysis of the servo position and roll rate. The rudder doublets exhibit a coupled roll-yaw response. On first actuation of the rudder, the aircraft typically rolls to a "# bank angle and yaws approximately $. The onset of opposite control input rolls the airplane quickly in the opposite direction with an additional yawing and pitching tendency. After the maneuver, the MAV is in a banked dive with several feet of altitude lost throughout the course of the doublet. As expected, the rudder appears to excite the dutch roll mode resulting in coupled roll and yaw response. Wing-shaping control doublets induce a different behavior of the MAV. The response of the airplane to wing shaping is similar in nature to responses from ailerons. Essentially, the aircraft response to the morphing is predominantly roll motion with little yaw or pitch coupling. Thus, the doublets are performed without considerable directional or altitude deviation. Following the completion of the maneuver, which resembles rocking the wings, the airplane is in a banked attitude. Recovery from the wing shaping doublet is considerably easier than that of the rudder doublet. Such a response indicates the wing shaping excites the roll convergence mode. Clearly, the MAV requires a stability augmentation system to facilitate operation and greatly expand its mission capability. In general, lateral maneuvers are particularly difficult because the MAV is so responsive. Small levels of actuation can easily achieve roll rate above 2 deg/s for these highly maneuverable vehicles. The introduction of a controller would lessen pilot workload for trajectory tracking and enable development of a vision-based autopilot system currently being designed [1]. The open-loop flight tests demonstrate the value of morphing for consideration of a stability augmentation system. The rudder can be used to generate lateral maneuvers but the tight coupling of roll and yaw complicates the control needed for trajectory tracking. Conversely, the morphing produces almost pure roll so an associated controller for tracking roll commands could be relatively simple. 5

6 4 Modeling 4.1 Parameter Estimation A model of the flight dynamics of the MAV is used to design the stability augmentation system. These models are necessarily developed by analysis of flight data because of theoretical difficulties. For instance, computational predictions of the aerodynamics are suspect for the low Reynolds numbers at which the MAV operates [5]. Also, the aeroservoelastic response of a membrane wing is challenging to predict. The model is therefore dependent on measurements taken during flight. The open-loop flight testing provided a set of data that is used for model identification. This data resulted from issuing a series of doublet commands separately to the rudder servo and the morphing servo. Examples of these doublets are shown in Figure 6. command time (s command time (s Figure 6: Doublet Commands to Rudder Servo (left and Morphing Servo (right A time-domain approach is used to estimate the dynamics relating the roll rate to the doublet commands. Specifically, the dynamics are initially represented as an autoregressive, moving-average (ARMA process [4]. The coefficients of this process are determined using standard regression analysis. The measurements of roll rate are used for system identification of the model. A set of these measurements is compared with the corresponding response generated by simulating the identified dynamics in Figure 7. Clearly the model is able to capture the general characteristics of the dynamics for these data sets. roll rate (deg/s roll rate (deg/s time (s time (s Figure 7: Roll Rate in Response to Doublet of Rudder Servo (left and Morphing Servo (right for Measured Data (%& and Estimated Data ( 6

7 ' Separate models are derived to represent the dynamics relating roll rate to the rudder and morphing servos for the MAV. These models are actually based on averages of the identified dynamics from each of the data sets resulting from 3 doublets to the rudder servo and 4 doublets to the morphing servo. Each model is realized as a state-space system whose elements are given in Table 3. actuation A B C D rudder morphing Table 3: Identified Roll Dynamics The models in Table 3 have a single state which is assumed to correspond to the roll convergence. Such an assumption seems justified given that morphing servo generated almost pure roll; however, the visual observation of the open-loop flight testing indicated the rudder servo excited the dutch roll mode more than the roll convergence. Higher-order models were identified for the data associated with the rudder servo but the singlestate model is clearly sufficient. The roll data needs to be augmented with yaw rate data to enable the 2-state dynamics of dutch roll to be identified. The dynamics are identified with different values of the state matrix or, alternatively, the time constant of the roll mode. The values are on the same order of magnitude for each identified model but are clearly different. This difference is expected because the wing is altered due to the morphing. Thus, the change in identified dynamics is a direct indicator of the change in aerodynamic characteristics. Also, different values of the input matrix are identified for each model. This result is entirely expected because the control effectiveness is clearly different between the actuation mechanisms. The morphing has a larger matrix value which indicates it is more effective in commanding rolling maneuvers than the rudder as evidenced by the larger magnitude for roll rate in Figure Lateral-Directional Model The dynamics given in Table 3 are obviously not sufficient to describe the complete lateral-directional dynamics of the MAV. Such complete models must include the dutch roll and spiral modes in addition to the roll convergence. The MAV does not have enough sensors to allow full-order estimation of the dynamics; therefore, the complete model is computed using an ad hoc approximation. A rough estimate of the complete dynamics is obtained by combining the partial models for this 1 in MAV in Table 3 with a complete model for a different 6 in MAV [8]. Obviously different types of MAV have different flight dynamics; however, the vehicles under consideration were of similar dimension with membrane construction for the wings. The model for the other MAV is based on a series of wind tunnel testing and is highly accurate [2, 7]. Several assumptions are used for model generation. One assumption is that the dutch roll mode of the 1 in MAV will have lower frequency and higher damping than the 6 in MAV because of pilot observations. Another assumption is that the current MAV will have low roll moment due to yawing because the aerodynamic center of the rudder is nearly level with the center of gravity. Also, the moments resulting from sideslip will be lessened on the 1 in MAV as compared to the 6 in MAV because of the vertical tail. The remaining assumptions deal with control surface effectiveness are based purely on pilot observations obtained during open-loop flight testing. 7

8 *. ( * 2 G The resulting model indicates the lateral-directional dynamics of the MAV. These dynamics correspond to the flight condition of sea level for altitude and 2 mph for airspeed or, equivalently, 1 psf for dynamic pressure. Again, note that this model is a crude approximation that will be refined after more flight tests. ( +,- / "#7 8 9:56"#; ; 9:56< =<> 51 =?" :56<8<>B =?"!51 8?"#; :5C>= ; 9:517 = ; 9:5D>= 8 :56 <;: :56<7:8 :56 < :56 E= 9:51;<>7 8 9:51=?"#;: :51=?"#;: :51=<>= :5A"#8 = 7 :56E@< :5A"# 8 :56<; ; 8 :51 7<> :56" "> :56"<<8 9:56<7 ;<> / FHGJI LKNMO KQPRSRUTVKXW The properties of this approximate model, both for modal dynamics and control effectiveness, correspond to observed flight characteristics. The model has eigenvalues which are somewhat large compared to many piloted airplanes given that the roll convergence has a time constant of.2 sec while the dutch roll mode has damping ratio of.121 and natural frequency of 1.68 Hz. Also, the model allows the morphing to excite the roll convergence much more than the dutch roll mode while the rudder is able to excite all modes. These properties for modal dynamics and control surface effectiveness agree with the open-loop characteristics observed during flight testing. Thus, the model is clearly an approximation but it serves as a reasonable representation to demonstrate the morphing concept for flight control. 5 Stability Augmentation System A controller is designed to affect the lateral-directional dynamics of the MAV. The motivating factor for designing this controller is to simplify the piloting of the MAV. Such a simplification would expand its mission capability by enabling more personnel to successfully operate the plane and even enabling autonomous operation. Several specific properties that are desired for the airplane are addressed by the controller. 1. The pilot should be able to command roll rate rather than actuator position. This scaling should allow pilots who are unfamiliar with the MAV to still fly the vehicle based on maneuvering principles. Also, this scaling will allow an outer-loop guidance and navigation controller to command maneuvers directly to this inner-loop stability augmentation controller. 2. The pilot should be able to easily perform fine tracking and gross acquisition. Such performance requires the response of the MAV to vary depending on the pilot command such that small commands generate disproportionately slower roll rates than large commands. 3. The MAV should have coordinated turns for maneuvering. The controller should allow the pilot to maneuver the aircraft by rolling and then pitching the MAV. Essentially, the pilot would command a normal acceleration to characterize the turn. 4. The MAV should have good handling qualities in nonlinear flight regimes. Specifically, the MAV is able to fly at angle of attack up to. The response at low and high angle of attack should be acceptable despite the different flight dynamics. 5. The MAV should have reasonable gust rejection. The controller should provide damping, particularly for the dutch roll mode, to alleviate the effects of uncommanded disturbances like gusts. 8

9 _ G K - The architecture for the controller, shown in Figure 8, has a traditional structure used for many aircraft.,zy I[I]\S^ G I h, R _ ` _Na _ b M _ b K _ cedgf Figure 8: Controller Architecture for MAV Each of the elements in Figure 8 is used to address the specific control objectives. The feedback filter, `, provides the command shaping enabling fine tracking and gross acquisition. The feedback element, b, acts M like a roll damper that may be scheduled with flight condition. The remaining feedback element, b, is a yaw K damper that affects the dutch roll mode and provides some measure of gust rejection. 6 Control Design The control system is currently being designed for the MAV. This current control system only considers the yaw damper. The remaining control elements, such as roll damper and feedforward filter, will be considered in the final version of the paper. The purpose of applying a yaw damper to the system is to increase the damping associated with the dutch roll mode. This increase is accomplished by using the rudder to create an opposite yaw moment in order to damp out the yaw from the dutch roll. The effects on the roll convergence while designing the yaw damper are also considered. The yaw damper is designed using the root locus plot of the system shown in Figure Imaginary Part of Poles Real Part of Poles Figure 9: Root Locus Plot for Yaw Damper The gain for the yaw damper is selected by its location on the bottom half curve of the root locus plot. The location of the gain is selected with a tradeoff between the damping ratio and the rudder deflection. As such, the gain selected does not correspond to the maximum damping ratio. The maximum damping ratio is not desirable because the controller will command too much rudder deflection and may actually dampen the mode too much 9

10 so i desired yaw commands can not be tracked. The gain selected is b K = which results in a corresponding 3 damping ratio increase to.78 but does not incur excessive rudder deflection. 7 Closed-Loop Simulation The flight characteristics of the MAV are demonstrated using a simulation of the approximate model. As such, the flight characteristics are limited to consideration of linear dynamics at a single flight condition. These simulations compute the open-loop and closed-loop responses to pilot commands and wind gusts. The response of the MAV to a rudder doublet is shown in Figure 1. The open-loop response shows unacceptable oscillations in both the roll rate and yaw rate due to the low damping of the dutch roll mode. The yaw damper has a considerable effect and removes most of the uncommanded oscillations from the closed-loop response open loop closed loop 6 4 open loop closed loop Roll Rate (deg/s Yaw Rate (deg/s Time (s Time (s Figure 1: Simulated Responses of the MAV to a Rudder Doublet A doublet is commanded to the morphing servo to generate the responses shown in Figure 11. The open-loop responses are acceptable for both roll rate and yaw and show only a small amount of oscillation due to the dutch roll mode. Inclusion of the yaw damping removes even these small oscillations so the closed-loop responses are improved beyond the open-loop responses. 3 2 open loop closed loop 4 2 open loop closed loop Roll Rate (deg/s 1 1 Yaw Rate (deg/s Time (s Time (s Figure 11: Simulated Responses of the MAV to a Morphing Doublet 1

11 The remaining simulation indicates the response of the MAV to a wind gust. The roll rate and pitch rate, as shown in Figure 12, are generated in response to a gust realized as an impulse lateral force. Clearly, the yaw damper greatly increases the gust rejection properties of the closed-loop system as compared to the open-loop dynamics. Roll Rate (deg/s open loop closed loop Yaw Rate (deg/s open loop closed loop Time (s Time (s Figure 12: Simulated Responses of the MAV to a Gust Impulse These simulations demonstrate the difficulty for remote piloting the MAV. The open-loop responses after any maneuver show oscillations resulting from the light damping of the dutch roll mode. Consequently, the pilot has a considerable workload to minimize the effects of the oscillations and follow a desired flight path. The open-loop response to a wind gust is particularly demonstrative. The MAV is quite small so wind gusts have a significant effect and, as observed in both the simulation and actual flight tests, the pilot must constantly move the control surfaces to cancel these disturbances. Similarly, the simulations demonstrate the benefits to automatic control for the MAV. The yaw damper, which is a simple controller, increases the damping of the dutch roll mode and reduces the oscillations observed in the responses. The closed-loop aircraft is certainly much easier to fly in terms of maneuvering and also gust rejection. Expanding the capability of this controller would almost certainly increase the performance capabilities of the aircraft. The morphing is a valuable control effector for the MAV. The current controller is able to use the morphing to command roll maneuvers and allow the rudder to provide damping of the dutch roll mode. Future designs could actually use the morphing for both roll and yaw control so the vertical tail could be completely removed. Also, the morphing could obviously be used for longitudinal control. 8 Closed-Loop Flight Tests Flight tests are on-going for the MAV to demonstrate the use of active morphing for roll control. The current instrumentation makes closed-loop control somewhat cumbersome; however, additional hardware is scheduled to arrive that will greatly simplify the process of automatic control. The results of these controlled flights are anticipated to be available for the final version of the paper. 11

12 j References [1] S.M. Ettinger, M.C. Nechyba, P.G. Ifju and M. Waszak, Vision-Guided Flight Stability and Control for Micro Air Vehicles, IEEE International Conference on Intelligent Robots and Systems, October 22, pp [2] G.A. Fleming, S.M. Bartram, M.R. Waszak and L.N. Jenkins, Projection Moire Interferometry Measurements of Micro Air Vehicle Wings, International Symposium on Optical Science and Technology, SPIE [3] P.G. Ifju, D.A. Jenkins, S. Ettinger, Y. Lian, W. Shyy and M.R. Waszak, Flexible-Wing-Based Micro Air Vehicles, AIAA [4] L. Ljung, System Identification, Prentice Hall, Englewood Cliffs, NJ, [5] T.J. Mueller, Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications, AIAA, Reston, VA, 21. [6] E.W. Pendleton, D. Bessette, P.B. Field, G.D. Miller and K.E. Griffin, Active Aeroelastic Wing Flight Research Program: Technical Program and Model Analytical Development, Journal of Aircraft, Vol. 37, No. 4, 2, pp [7] M.R. Waszak, L.N. Jenkins and P. Ifju, Stability and Control Properties of an Aeroelastic Fixed Wing Micro Aerial Vehicle, AIAA [8] M.R. Waszak, J.B. Davidson, and P.G. Ifju, Simulation and Flight Control of an Aeroelastic Fixed Wing Micro Aerial Vehicle, AIAA